Question

Tie am of the digits of a two digit number is 9. If 9 is added to the number formed by reversing the digits, then the result is thrice the orientation number. Find the original number

Answer 1

let the ones digit be x
&tens digit be y
the 2 digit no. will be 10y + x
given that, x+y = 9.......(1)
and reverse digit will be 10x + y
ATQ
9 + 10x + y = 3(10y + x)
9 + 10x + y = 30y + 3x
= -7x + 29y = 9.........(2)
now we solving the eqn. therfore we have to multiply eqn 1 by -7
eqn 1 become -7x -7y = -63 .....(3)
subtracting eqn(2)-eqn(3)
=36y = 72
y = 2
putting value of y in eqn(1)
x + 2 = 9
x = 7
so the 2 digit no. is 10y + x = 10×2 + 7
= 27
The number is 27
I HOPE THIS IS HELPFUL